Closed Itemset Mining and Non-redundant Association Rule Mining
نویسنده
چکیده
DEFINITION Let I be a set of binary-valued attributes, called items. A set X ⊆ I is called an itemset. A transaction database D is a multiset of itemsets, where each itemset, called a transaction, has a unique identifier, called a tid. The support of an itemset X in a dataset D, denoted sup(X), is the fraction of transactions in D where X appears as a subset. X is said to be a frequent itemset in D if sup(X) ≥ minsup, where minsup is a user defined minimum support threshold. An (frequent) itemset is called closed if it has no (frequent) superset having the same support. An association rule is an expression A ⇒ B, where A and B are itemsets, and A ∩ B = ∅. The support of the rule is the joint probability of a transaction containing both A and B, given as sup(A ⇒ B) = P (A ∧ B) = sup(A ∪ B). The confidence of a rule is the conditional probability that a transaction contains B, given that it contains A, given as: conf(A ⇒ B) = P (B|A) = P (A∧B) P (A) = sup(A∪B) sup(A) . A rule is frequent if the itemset A∪B is frequent. A rule is confident if conf ≥ minconf , where minconf is a user-specified minimum threshold. The aim of non-redundant association rule mining is to generate a rule basis, a small, non-redundant set of rules, from which all other association rules can be derived.
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